Life Insurance¶

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Before you startEarlier concepts these pages use most. If a step feels unfamiliar, revisit them first.3 courses

Probability Theory for EOR

Probability Distributions

Math I: Calculus

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How to read this courseNotation, shared pages and conventions

These notes introduce course-specific concepts. Existing Year 1 concepts have one canonical page and are linked under Before you start. The lecture sequence follows the 2026 course outline, with one lecture in each of the seven teaching weeks. Concepts appear at their first introduction and are reused by links afterwards.

Actuarial notation¶

The term angle $\actuarialterm{n}$ means an $n$ -year term. Its horizontal bar and right-hand stroke mark the duration, while the variable $n$ keeps its usual mathematical font.

Symbol	Meaning	Markdown formula
$v$ , $d$ , $\delta$	Discount factor $v=(1+i)^{-1}$ $i)^{- 1}$ , discount rate $d=1-v$ and force of interest $\delta=\log(1+i)$ at annual effective interest $i$	`$v$, $d$, $\delta$`
$\ddot a_{\actuarialterm{n}}$	Annuity certain, payable in advance	$\ddot a_{\angl{n}}$
$\ddot a_{x:\actuarialterm{n}}$	Temporary life annuity-due	$\ddot a_{x:\angl{n}}$
$\bar a_{x:\actuarialterm{n}}$	Continuous temporary life annuity	$\bar a_{x:\angl{n}}$
$A_{x:\actuarialterm{n}}$	Endowment insurance, annual settlement	$A_{x:\angl{n}}$
${}_{u\mid}\ddot a_x$	Deferred life annuity-due	${}_{u\mid}\ddot a_x$
${}_np_x$ , ${}_nq_x$	Survival and death probabilities	`${}_np_x$, ${}_nq_x$`
${}_nE_x$	Pure endowment factor	${}_nE_x$
${}^{2}A_x$	Second moment of whole life insurance present value	${}^{2}A_x$
$l_{[x]+t}$	Select-table survivors after duration $t$	$l_{[x]+t}$

Payment timing and benefit conditions are defined on each concept page. A bar above $a$ or $A$ indicates continuous payments or settlement at death; the two dots on $a$ indicate payments in advance.

SourcesCourse material these pages were checked against

Life Insurance · Course outline (2026)
Life Insurance · Lectures 1–7

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Aliases: LI Symbols: delta

Last updated: 26 October 2026 00:09